Question

Eliminate theta from the following x =3sec theta y = 4tan theta

Answer 1

Answer:

Step-by-step explanation:

3sectheta y=4tan theta

3y/cos theta=4sintheta/cos theta

3y=4sintheta

Theta=sin inverse(3y/4)

Answer 2

Answer:

After eliminating theta we get the result:

$\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$

Step-by-step explanation:

Given equation is:

$x=3sec\theta$

And,

$y=4tan\theta$

We can write as:

$sec\theta=\dfrac{x}{3}$

And,

$tan\theta=\dfrac{y}{4}$

Hence now we are applying trigonometric formula and it has been shown below:

$sec^2\theta-tan^2\theta=1$

Substituting the value of $sec\theta$ and $tan\theta$ in above formula:

$(\dfrac{x}{3})^2-(\dfrac{y}{3})^2=1\\\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$